The Electron-Volt Chain — Lattice Derivation

An energy is a count of time and the electron-volt is a clock: from the electron through the fine structure constant to hydrogen's quantum, its shells, its lines and the bonds of chemistry

13.6048896 eV (2⁸·3¹²/10⁷) electron × α² ÷ 2 Hβ 2.5509168 eV × 486 nm = 2⁵·3¹⁸ 13 pages · 8 plates

Three roads to one number

Hydrogen's quantum on the G1 register is reached three independent ways, every one exact.

THE ELECTRON ROAD
511,280.83701927 (2⁹·3⁸·5⁶·π⁴/10⁷) × α² ÷ 2 = 13.6048896 eV (2⁸·3¹²/10⁷) — every π gone
THE FLASK ROAD
1312.2 kJ/mol (3⁸/5) ÷ 96.450617283950617 = 13.6048896

One joule, five volts

The volt is not a constant. One joule read through five lattice volts gives five faces of hydrogen: sodium 13.6085694, G2 13.6061161 (the ground state), G1 13.6048896, face 2 13.5977828 and face 1 13.5965571.

The ladder and the lines

Each shell is the quantum over n²; multiply back by n² and the quantum returns. The lines are fractions of it.

THE LINES
Lyman-α 10.2036672 · Hα 1.889568 · Hβ 2.5509168
Hβ 2.5509168 × 486 nm = 1239.7455648 (2⁵·3¹⁸/10⁷)

Questions This Paper Answers

Why is hydrogen's ionisation energy 13.6 eV?

It is the electron, 2⁹·3⁸·5⁶·π⁴/10⁷ eV, geared down twice by α and halved: 13.6048896 = 2⁸·3¹²/10⁷, a pure count with no π.

What is an electron-volt in the Universal Force of Time?

A choice of clock: an energy is a count of time, and the electron-volt reads it on the spin-orbit register of the atom.

What is the H–H bond energy in electron-volts?

432 kJ/mol ÷ the Faraday = 4.478976 eV (2⁵·3⁷/5⁶).

Open Academic PDF ↗ All Papers ← Home
A note on the numbers. Every value here is given at full precision, because the precision is the evidence. A quantity truly on the {2,3,5,π} lattice does not approximate a lattice form; it is one. Where a value has not been read onto the lattice we say so rather than rounding until it appears to fit. And a number in this framework is not a measurement of one thing: it is one address that may surface as a period, a frequency, a radius, an energy or a proportion, depending only on the register in which it is read — the same register carries Mercury's orbit and the radio line of hydrogen.

Nothing on this page was pulled, attracted or held down. There is one substance — time — flowing from the sparse toward the dense, and the radio whisper of cold hydrogen and the slow turning of Mercury are one thread of its pattern. If it stirred your curiosity, the whole weave is waiting: the planets, the atom, light, life and number, all carried by the same single force.

Read the whole theory of the Universal Force of Time →